Labor's cheap, materials are cheap, land is ridiculously expensive. Everywhere on the island, apparently.

Why is all the land so expensive? Who owns it all?

The island is very densely populated! Several million people, and it's not a big island, and there are lots of estates and lots of neighborhoods and the crown in fact owns a lot of land.

Wow. It's amazing that they manage to feed everyone while so space-constrained. As a matter of fact, this looks like just the place that could use synthetic nitrogen fertiliser - especially since plant-eaters would be able to consume the crops directly, instead of through animal intermediaries. She'll have to compare the relative value of these enterprises to decide where to start. She looks up crop yields and food prices.

Food is indeed pretty expensive and a major expense, and lots of the land is low-yield after thousands of years of cultivation.

Now, if only she remembered more chemistry. All she knows for sure is that the nitrogen-fixation process requires passing hydrogen and nitrogen over an iron catalyst at high temperature and pressure, and she only recalls that much because a schematic was included in a chapter on the Silesian War - oh, right, ammonium makes bombs too. Crap. She'll need to see whether this country has ammonium-intensive weaponry yet. If so, giving them a way to produce cheap ammonium might not be a good idea right now.

She makes a note and then goes on to investigate the current state of military technology here. If Adûna isn't an ammonium-constrained genocide waiting to happen, then she'll go ahead and grab some chemists to experimentally determine what combination of temperature/pressure/iron produces agricultural miracles.

They do already have gunpowder and some kind of bombs; the kind isn't immediately apparent, unless she can read a lot of ship diagrams with very technical language.

Carmen cannot into ships! She accepts that this is probably worth it for the sake of feeding people and gaining the political power she'd need to halt colonisation. After all, they don't seem particularly ammonium constrained, such that a new source would lead to a surge in military power.

...But, just in case, she keeps looking into other useful potential industries. What do people use for fuel, and how do they access it? Wait, they do have steam engines, right? She'd been assuming, because some amount industry clearly exists, but she should really check.

Yes to steam engines, though not super widely, There's no coal native to the island, it's all imported.

Do they use oil or natural gas at an industrial scale? Do they have any sources thereof on the island?

No, and because they don't use it it's hard to tell if there are any sources. Probably not, though, since the island was raised out of the sea a few thousand years ago - the same reason there's no coal.

Huh. What even is the composition of this island? Volcanic stone? Limestone from an upraised coral reef?

How far away is the mainland? What resources are present in the colonies? Are there smaller islands nearby to Adûna?

No islands near Adûna. The outlying islands of Valinor are nearby but Men are Not Allowed there; there's no islands between here and the mainland on the other side, which is eight hundred or so miles away.